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Answer :
To solve this problem, let's break it down step-by-step.
1. Understanding the Problem:
- We have been given a statement: "The sum of two consecutive integers is 143."
- We need to form an equation to represent this statement.
2. Defining Variables:
- Let the first integer be [tex]\( x \)[/tex].
- The next consecutive integer would be [tex]\( x + 1 \)[/tex].
3. Forming the Equation:
- According to the problem, the sum of these two integers is 143.
- So, the equation that represents the statement is:
[tex]\[
x + (x + 1) = 143
\][/tex]
4. Solving the Equation:
- Combine the terms on the left side:
[tex]\[
x + x + 1 = 143 \Rightarrow 2x + 1 = 143
\][/tex]
5. Isolating [tex]\( x \)[/tex]:
- Subtract 1 from both sides of the equation:
[tex]\[
2x = 142
\][/tex]
- Divide both sides by 2 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = 71
\][/tex]
6. Identifying the Consecutive Integers:
- The first integer is [tex]\( x = 71 \)[/tex].
- The next consecutive integer is [tex]\( x + 1 = 71 + 1 = 72 \)[/tex].
So, the two consecutive integers whose sum is 143 are 71 and 72. The correct equation from the options provided is:
[tex]\[
x + x + 1 = 143
\][/tex]
1. Understanding the Problem:
- We have been given a statement: "The sum of two consecutive integers is 143."
- We need to form an equation to represent this statement.
2. Defining Variables:
- Let the first integer be [tex]\( x \)[/tex].
- The next consecutive integer would be [tex]\( x + 1 \)[/tex].
3. Forming the Equation:
- According to the problem, the sum of these two integers is 143.
- So, the equation that represents the statement is:
[tex]\[
x + (x + 1) = 143
\][/tex]
4. Solving the Equation:
- Combine the terms on the left side:
[tex]\[
x + x + 1 = 143 \Rightarrow 2x + 1 = 143
\][/tex]
5. Isolating [tex]\( x \)[/tex]:
- Subtract 1 from both sides of the equation:
[tex]\[
2x = 142
\][/tex]
- Divide both sides by 2 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = 71
\][/tex]
6. Identifying the Consecutive Integers:
- The first integer is [tex]\( x = 71 \)[/tex].
- The next consecutive integer is [tex]\( x + 1 = 71 + 1 = 72 \)[/tex].
So, the two consecutive integers whose sum is 143 are 71 and 72. The correct equation from the options provided is:
[tex]\[
x + x + 1 = 143
\][/tex]
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